Modern operations for the exploration and production of oil and gas rely on access to a variety of information regarding parameters and conditions encountered downhole. Such information typically includes characteristics of Earth formations traversed by a borehole, as well as data relating to the size and configuration of the borehole itself. The collection of information relating to subsurface conditions, which is commonly referred to as “logging,” can be performed by several methods, including wireline logging and logging while drilling (LWD).
In wireline logging, a sonde is lowered into the borehole after some or all of the well has been drilled. The sonde hangs at the end of a wireline cable that provides mechanical support to the sonde and also provides an electrical connection between the sonde and electrical equipment located at the surface. In accordance with existing logging techniques, various parameters of the Earth's formations are measured and correlated with the position of the sonde in the borehole as the sonde is pulled uphole. In LWD, a drilling assembly includes sensing instruments that measure various parameters as the formation is penetrated, thereby enabling measurement of the formation during the drilling operation.
Among the available wireline and LWD tools are a variety of resistivity logging tools including multi-array laterolog tools. Such tools typically include a central electrode around a tool body, with guard electrodes spaced above and below the central electrode. The tool drives auxiliary currents between the guard electrodes and the central electrode to focus the current from the center electrode, i.e., to reduce dispersion of the current from the central electrode until after the current has been located some distance into the formation. Generally speaking, a greater depth of investigation can be achieved using more widely-spaced guard electrodes, but the vertical resolution of the measurements may suffer. Accordingly, existing tools employ multiple sets of guard electrodes at different spacings from the center electrode to enable multiple depths of investigation (DOI) without unduly sacrificing vertical resolution. In this context, depth of investigation refers to a depth parameter that extends radially relative to the longitudinal axis of the borehole. Multi-array laterolog tool systems thus offer multiple depths of investigation, which is particularly useful in borehole environments having significantly variable depth-wise resistivity profiles.
Collected measurements from multi-array laterolog tool systems are often processed to determine overall measurement zone resistivity logs at multiple depths of investigation. These resistivity measurements typically indicate, however, overall resistivity in a subsurface zone surrounding the borehole, which does not necessarily correspond to the resistivity of an underlying geological formation through which the borehole extends, because the measured subsurface zone can include an invasion zone resulting from the drilling/exploration operation. Resistivity values for the measurement zone overall are often expressed as being dependent on three fundamental parameters, namely the true resistivity of the geological formation, the resistivity of the invasion zone, and the radial depth of the invasion zone. As a result, calculating the true values for these three parameters from a single measured value presents an ill-posed problem that calls for significant processing resources and that can be significantly sensitive to initial guessed values for at least some of the parameters.